GATE MA format:nat PYQs & Answers — Page 4

Questions 31–40 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 4 of 23

Let

be distinct non-zero real numbers, and let

be a polynomial of degree less than 5. If the function

satisfies Morera’s theorem in

, then the value of

is equal to _____ (in integer)

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Let

be a group with identity element

, and let

be such that the following hold:

(i)

(ii)

, and

Then, the least positive integer

for which

is _____ (in integer)

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Let

and

be two metric spaces with

and

If the open ball centred at

with radius

is equal to the open ball centred at

with radius

, then the value of

is _____ (in integer)

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Let

and

be a differentiable function such that

and

, for every

and

. The value of

is equal to ______ (answer in integer)

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The number of non-isomorphic finite groups with exactly 3 conjugacy classes is equal to ______ (answer in integer)

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Let

, where

. Let

be the inverse of

in a neighborhood of

. Then the determinant of the Jacobian matrix of

is equal to ______ (round off to TWO decimal places)

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Let

be the field with exactly 3 elements. The number of elements in

is equal to ______ (answer in integer)

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Given a real subspace

, let

denote its orthogonal complement with respect to the standard inner product on

. Let

and

be real subspaces of

. The dimension of

over

is equal to ______ (answer in integer)

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The number of group homomorphisms from

is equal to ______ (answer in integer)

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Let

and

be a positive real number. For any twice-differentiable function

, let

be the interpolating polynomial of degree at most two that interpolates

at the points

. Define

to be the largest integer such that any polynomial

of degree

satisfies

The value of

is equal to ______ (answer in integer)

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GATE MA format:nat PYQs

Question 63

Question 64

Question 65

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32